The present invention relates to the display of electrical signals, and more particularly to an improved interpolation of sampled complex signals for increasing the accuracy of the displayed signal.
There are many demands for observing the envelope magnitude of a radio frequency (RF) band-limited signal in the time domain. Modern measurement instruments, such as spectrum analyzers as represented in FIG. 1, measure the magnitude of the RF band-limited signal from the sampled signal. To measure intermediate points between the sampled points of the signal, some interpolation is commonly used. Ideal interpolation is reconstructing intermediate points from the discrete samples. One of the optimal methods for band-limited signals is resampling. However a traditional interpolation technique, such as a cubic spline interpolation, is still popular although the signal reconstruction is not perfect. A traditional interpolation technique may be more desirable when interpolation points are irregularly spaced, when faster speed is required, and/or when it is difficult to design a reconstruction filter for the resampling method.
There are two common methods for computing the magnitude of interpolated complex signals using traditional techniques. However both methods have some difficulties. One method is to take the magnitude of the original sampled signal and then apply interpolation, as shown in FIG. 2. This first method may produce negative interpolated data, as shown in FIG. 3. The other method is to apply interpolation separately to In-phase and Quadrature-phase components of the signal and then compute the magnitude, as shown in FIG. 4. This second method does not produce negative magnitudes, but may introduce excessive ripple if the signal phase is rotating, as shown in FIG. 5. If linear interpolation is used for the phase rotating signal, the cause of the introduced ripple in the magnitude trace is apparent, as shown in FIG. 6.
What is desired is an improved interpolation for complex signals that does not produce negative magnitudes and does not introduce excessive ripple in order to provide a more accurate representation of the input signal.